Why grant the name change for these users if this was going to be the result?
I'm almost certain that most name changes aren't done to hide who they are. I mean, if you fucked up in the past and change your name to hide that, there will always be quotes off your old name. Plus trust feedback and flags don't change, so what's the point in doing that? The only way to truly start over is to create a new account.
A name change will, of course, still increase your privacy a little bit, but all I'm trying to say is that there will always be posts that contain your old name. Maybe even positive trust ratings where they mention your old name.